One of our cats will pick up your hand in their mouth (not biting) and bring it back over to where you were petting.
My dog wedges his head in under my phone holding hand and replaces my screen with his face. Okidoki then my beloved boy. I play with you.
After I taught my cat to shake paws, she started coming up to us and offering her paw to us. She'll either place her paw on us / on our hands or paw at the air in front of us.
One of our cats will pick up your hand in their mouth (not biting) and bring it back over to where you were petting.